A local Fourier transform of a wave field is an integral transformation from space-time coordinate space to phase space, i.e., ray parameter, spatial coordinate, and intercept- time space. McMechan (1983) introduced the concept of a local slant-stack/Fourier transform. Using this integral transform, he was able to define a wave field in phase space. By projecting the resulting wave field to the spatial coordinate space, he obtained a representation of the wave field in the ray-parameter and the spatial-coordinate plane. In this paper, the local Fourier method is used to transform the Helmholtz wave equation into a phase-space coordinate system. The resulting wave equation is then written in a state-variable form of coupled first-order differential equations. A propagator solution is then shown.

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